Distinctive mechanisms of epilepsy-causing mutants discovered by measuring S4 movement in KCNQ2 channels

Neuronal KCNQ channels mediate the M-current, a key regulator of membrane excitability in the central and peripheral nervous systems. Mutations in KCNQ2 channels cause severe neurodevelopmental disorders, including epileptic encephalopathies. However, the impact that different mutations have on channel function remains poorly defined, largely because of our limited understanding of the voltage-sensing mechanisms that trigger channel gating. Here, we define the parameters of voltage sensor movements in wt-KCNQ2 and channels bearing epilepsy-associated mutations using cysteine accessibility and voltage clamp fluorometry (VCF). Cysteine modification reveals that a stretch of eight to nine amino acids in the S4 becomes exposed upon voltage sensing domain activation of KCNQ2 channels. VCF shows that the voltage dependence and the time course of S4 movement and channel opening/closing closely correlate. VCF reveals different mechanisms by which different epilepsy-associated mutations affect KCNQ2 channel voltage-dependent gating. This study provides insight into KCNQ2 channel function, which will aid in uncovering the mechanisms underlying channelopathies.


Introduction
Voltage-gated K + (Kv) channels play a crucial role in regulating excitability and dysregulation of their function has been associated with several disorders, including cardiac arrhythmias, epilepsy and autism. Kv channels, including all members of the Kv7 family (Kv7.1-Kv7. 5, also known as KCNQ as they are encoded by KCNQ1-5 genes (1-3)), are highly heterogenous and widely expressed in excitable cells where they regulate resting membrane potential, shape the firing and duration of action potentials, and control rhythmic events(4).
One of the major potassium currents throughout the central and peripheral nervous systems is the muscarine-regulated M-current. The M-current is mainly conducted by heterotetrameric combinations of KCNQ2/3 and KCNQ3/5 channel (5)(6)(7)(8), but homotetrameric assemblies of channel subunits have also been shown to function as the M-current in neurons (8,9). KCNQ are noninactivating channels with slowly activating and deactivating kinetics and a negative voltage for halfactivation (5,6). These biophysical properties make KCNQ channels important regulators of neuronal excitability. For example, the peculiar lack of inactivation at voltages near the threshold for action potential initiation confers KCNQ channel's dominant role in regulating membrane excitability as one of the main outward sustained currents. Thus, inhibition of the KCNQ channel lowers the action potential threshold, increase afterdepolarization(10), and slows excitatory postsynaptic potentials (11), resulting in a reduced adaptation and prolonged repetitive neuronal firing (12). Among the KCNQ family of proteins, KCNQ2 channels have received particular attention because mutations in this channel cause a variety of neurodevelopmental phenotypes (2,13,14), including epileptic encephalopathy (15)(16)(17)(18)(19)(20), and more recently autism (21). Since KCNQ2 channels are central to physiological and pathophysiological events, it is important to understand the voltage-dependent mechanisms underlying channel opening to define its role in physiological control of neuronal excitability and to understand how specific variants alter KCNQ2 channel function.
The recently elucidated cryo-EM structure of human KCNQ2 channels (22) shows that, like canonical Kv channels (23), KCNQ2 contains six transmembrane helices (S1-S6) with cytosolic oriented N-and C-termini that form functional tetramers. The S5-S6 of the four subunits form a centrally located potassium selective pore that is flanked by the four voltage-sensing domains (S1-S4) (23). KCNQ2 has a domain-swapped tetrameric architecture, where the C-terminal end of the S6 segments form the gate (23,24). The fourth transmembrane segment is assumed to be the voltage sensor (S4) since it contains several highly conserved positively charged amino acid residues.
Although the S4 has been shown to move in response to changes in membrane voltages and functions as the voltage sensor in other Kv channels (25)(26)(27)(28), this has not yet been directly demonstrated for KCNQ2 channels. Gating current recordings have not been resolved for KCNQ2 channels, likely due to low channel density within the membrane and/or the slow kinetic of activation compared to other Kv channels (29). Insight into S4 movement of KCNQ2 have been inferred by previous mutagenesis studies showing that charge neutralization of the arginine residues in S4 altered the voltage sensitivity of channel opening (30,31). In addition, a disulfide crosslinking study showed that cysteine-substituted residues in the extracellular end of S4 crosslinked with a cysteine in S1 only in the closed state, further implying movement of S4 (32). Although these studies provided insight into S4 rearrangements, they were unable to explain how S4 moves, nor were they able to offer a dynamic view of S4 motion during voltage-controlled gating of KCNQ2 channels.
Our understanding of the voltage-controlled activation mechanisms of KCNQ2 channels is limited, compared to other Kv channels like the related KCNQ1, whose physiological role in cardiac tissue has been extensively investigated (33). Kv channel opening can occur either after all four S4 have been activated (34), or alternatively through independent activation of each S4 (35), as also reported for KCNQ1 (36). Interestingly, pore opening of KCNQ1 channels can occur from two defined S4 conformations involving intermediate and fully activated S4 states (37)(38)(39). This activation scheme in which opening may occur from multiple S4 states, has provided a valuable framework to understand voltage-dependent gating of KCNQ1 with different accessory subunits, thereby allowing interpretation of its versatile physiology. Because we lack mechanistic understanding of voltagedependent gating in neuronal KCNQ2 channels, it is not clear what mechanisms could be altered in the presence of disease-causing mutations. We here describe mechanisms underlying voltage sensor movement in KCNQ2 channels and propose a simple model of channel opening as it relates to epilepsy-associated mutations.
We provide an extensive exploration of positions where cysteine could be inserted into the S3voltage sensor (S4) loop and S4 helix and used with both voltage clamp fluorometry (VCF)(25) and cysteine accessibility (26) to study S4 activation and its influence on disease causing mutations.
Cysteine accessibility reveals that a stretch of 8-9 S4 residues becomes exposed upon opening of KCNQ2 channels. VCF shows that the voltage dependence and kinetics of S4 movement and channel opening/closing closely correlate. Our gating scheme suggests that multiple voltage sensor movements are not required to open KCNQ2 channels. VCF data and kinetic modelling shows that two epilepsy-causing mutations-R198Q and -R214W alter channel opening through two distinct mechanisms: R198Q shifts S4 movement and R214W changes the voltage sensor-to-pore coupling.
These results provide critical information about KCNQ2 channel gating that will aid in future studies on KCNQ2 channelopathies.

Results
State-dependent external S4 modifications consistent with S4 as voltage sensor.
The combination of cysteine-scanning mutagenesis and methanethiosulfonate (MTS) derivative modification is a powerful tool to study conformational changes in ion channel gating. This methodology assumes that upon covalent modification of substituted cysteines, functional changes in channel gating occur ( Figure 1A). We test whether the fourth transmembrane domain (S4) in KCNQ2 channel functions as the voltage sensor by measuring the state-dependent accessibility changes of introduced cysteines in the S4 (or in the S3-S4 linker) of KCNQ2 channels ( Figure 1A-C). We assess the state-dependent modification rate of substituted cysteines by plotting the membrane-impermeable thiol reagents (MTS)-induced change in current against the cumulative exposure to MTS reagents at either hyperpolarized (closed) or depolarized (open) voltages (See materials and methods section and voltage protocols in Figure 1B). As previously used to demonstrate that the S4 crosses the membrane during gating of the Shaker channel(26), we assume that changes in the state-dependent modification rate of substituted-cysteines by externally applied MTS compounds would indicate that some residues in S4 move (outward) across the membrane during channel activation.
In total, we made 8 cysteine mutants within the S4 (or in the S3-S4 linker) of KCNQ2 channels values (as also shown earlier for HCN1 channels (40), Figure 1D, E), as if N190C is always accessible and exposed to the extracellular solution ( Figure 1K, yellow). For R198C, external MTSET application in the open state (at +20-mV) irreversibly speeds up the kinetics of activation, increases the current amplitude, and left-shifts the G(V) relationship ( Figure 1F-G, red). In contrast, when MTSET is applied in the closed state (at -80-mV), R198C channels are not modified ( Figure 1F-G, gray). Since MTSET modifies residue R198C relatively fast at depolarized potentials ( Figure 1J, J', red) but not significantly at hyperpolarized potentials ( Figure 1J, J'', gray), that suggests that this residue is not accessible (i.e. is buried in the membrane) in the closed state (with S4 down) but becomes accessible in the open state (with S4 up, Figure 1K, red). Note that the perfusion system quickly delivers a 5-s pulse of MTS-reagents to the external surface of oocytes. This ensures perfusion of MTS-reagents at the indicated voltage as shown by the time course of solution exchange from 100 mM NaCl to 100 mM KCl (Figure 1-figure supplement 2). We find similar state-dependent modifications upon external MTSET perfusion for KCNQ2 channels with the S4-mutations A193C, S195C, A196C, S199C, and L200C (  Table 1). Similar gating sensitivities have been shown for homologous cysteine mutations in KCNQ3 channels (42).
Of the five labeled KCNQ2 substituted cysteines, the mutant KCNQ2-F192C (henceforth called KCNQ2*) shows the most reliable and robust voltage-dependent fluorescence signals (maximum fluorescence change, dF/F ∼1%) that saturates well at negative and positive voltages, either labeled with Alexa488 5-maleimide ( Figure 2B Figure 2C and supplement Table 1). The fluorescence signals in Figure 2B have a non-linear voltage dependence and are much slower than the voltage changes per se, which suggests that the fluorescence changes are not electrochromic responses of the dye to voltage changes. Instead, these results suggest that the fluorescence changes around labeled F192C at the outer end of S4 are due to conformational changes of the S4 segment related to the opening and closing of the KCNQ2 channel gate.
Next, VCF was used to compare the time courses of fluorescence signals and ionic currents of KCNQ2* channels during both depolarization-induced activation and repolarization-induced deactivation ( Figure 3). We use a pre-pulse to −120-mV to completely close the channel before stepping to test voltages ( Figure 3A, E). The fluorescence signal decreases in response to the prepulse to −120-mV ( Figure 3A, E, cyan arrow), indicating that not all voltage sensors are in their resting position at the −80-mV holding potential. We find that both ionic currents and fluorescence signals follow a double exponential time course in response to a family of voltage steps between −60 and +40-mV following the pre-pulse at −120-mV ( Figure 3A, B). The fluorescence signal only slightly precedes the ionic current. While the voltage-dependence of the fast fluorescence component is smaller than the slow component, it shows clear differences between extreme voltages (Fig. 3C).

S4 accessibility supports voltage-dependent motion of the S4 segment.
We test whether the voltage-dependent fluorescence signals measured with VCF faithfully report on the S4 movement. We took advantage of the state dependent modification of A193C by MTSET ( Figure 1-figure supplement 1F, G) to measure the rate of access to MTSET at different voltages as an independent assay ( Figure 4). External MTSET modification speeds up the activation of A193C channels and increases the current amplitude ( Figure 4B). While MTSET modifies A193C channels at voltages more positive than −100 mV ( Figure 4B, C), MTSET, however, modifies A193C 5-fold faster at +20-mV than at −100-mV ( Figure 4C and supplement Table 1). The modification rate for A193C approaches zero between −140 mV and −160-mV, as if A193C is inaccessible at those voltages ( Figure 4D). The voltage dependence of modification rate by MTSET (modification rate/voltage curve or 'mod. rate(V)') follows the conductance/voltage curve G(V) for A193C channels (mod. rate(V) = -72.7 ± 19.6 mV, n = 3-8 and G(V) = -66.4 ± 1.95 mV, n = 8, Figure 4D). The mod. rate(V) of A193C has similar voltage dependence as the F(V) of KCNQ2* channels (F(V) = -87.1 ± 3.9 mV, n = 7, Figure 4E, as if the fluorescence accurately reflects on S4 movement.

Disease-causing mutations differentially affect S4 and gate domains.
Next, we took advantage of the epilepsy-causing mutations R198Q and R214W in KCNQ2 channels (43,44) to further test if the voltage-dependent fluorescence changes around labeled F192C correspond to S4 motion. R198Q, which neutralizes the first gating charge of S4 in KCNQ2 channels ( Figure 5A), was previously shown to shift the G(V) to more hyperpolarized potentials, to accelerate the kinetic of activation and to slow down kinetic of deactivation (43). We reason that if the fluorescence signal of the KCNQ2* channel observed in Figure 2 indeed reports on S4 movement, KCNQ2* bearing R198Q would similarly shift the F(V) curve to negative voltages and affect activation and deactivation kinetics. We find that the KCNQ2*-R198Q mutation causes a hyperpolarizing shift in the G(V) curve, slightly speeds up the kinetic of activation, and slows the kinetics of deactivation ( Figure Figure 5C). These results further suggest that the fluorescence signal from F192C channels tracks the voltage-sensing rearrangement of S4 that controls channel opening, assuming that the R198Q mutation directly affects movement of the S4.
In contrast to R198Q, the R214W mutation was previously reported to shift the G(V) relationship to more depolarized voltages (44). Compared to KCNQ2*, KCNQ*-R214W channels display a rightward shifted G(V) curve (ΔG1/2 = + 60-mV ± 1.8 mV, Figure 5E reported for R214W channels (44). VCF shows that in R214W channels, the time course of fluorescence signal precedes the time course of ionic current ( Figure 5D and D'). Interestingly, the F(V) curve of R214W, which is + 10-mV shifted compared to the F(V) curve of KCNQ2* channels, is markedly leftshifted compared to its G(V) curve ( Figure 5E). These results indicate that R214W seems to mainly affect the S6 gate and not directly the S4 segment. The separation between F(V) and G(V) suggests that, like the uncoupling mutation F351A in KCNQ1 channels (36,37,45) or the ILT mutation in the Shaker K + channels(46), R214W dissociates voltage sensor movement from channel opening.
Collectively, our results on the R198Q and R214W mutations provide additional support that the fluorescence signals observed from KCNQ2-F192C labeled with Alexa-488-maleimide are indeed reporting on voltage-gated conformational changes in the S4 preceding channel opening and not on voltage-gated conformational changes in other domains of the channel, such as gate opening.
Furthermore, we hypothesize that since R214W is in the loop connecting S4 to the S4-5 linker (not within the voltage sensor, Figure 5-figure supplement 2A), it will most likely affect the activation gating without directly affecting S4 movement.

Kinetic Model for KCNQ2 channel gating
We use the two protocols in Figure 3 Figure 6F, gray) as channels seem to fully close at voltages more negative than −140 mV ( Figure 2). We simulate KCNQ2 gating using the calculated rate constants and voltage dependences from  Figure 6H). By decreasing the opening transition (L in Figure 6F) relative to wt KCNQ2 channels, the model also describes the clear separation between F(V) and G(V) curves observed in mutated KCNQ2*-R214W channels ( Figure 6H), under the assumption that R214W changes the voltage sensing domain-pore domain (VSD-PD) coupling such that it prevents opening before multiple S4 have activated ( Figure 6F, dashed maroon arrow). Additionally, data from the R198Q mutation can also be simulated by shifting the voltage dependence to negative voltages. This model suggests that for wt-KCNQ2 channels, all four voltage-sensor movements are not required before gate opening. In contrast, R214W seems to require multiple transitions of voltage sensors between closed states before channel opening. This gating scheme represents a starting point to understand the voltage-sensing mechanisms that are coupled to KCNQ2 activation as well as the functional effects of disease-causing mutations.

Discussion
In this paper, we provide functional data that support the hypothesis that the fourth transmembrane segment (S4) in KCNQ2 channels acts as the voltage sensor that promotes channel opening. Our fluorescence measurements show a close correspondence between the voltage sensor movement and channel opening in KCNQ2 channels as both voltage dependence and the time courses of fluorescence and ionic current closely correlate. VCF, mutagenesis, and kinetic modeling suggest that in KCNQ2 channels multiple voltage-sensor movements are not required to open the gate. We find that two epilepsy mutants cause shifts in voltage dependence of channel opening by two different mechanisms: R198Q shifts S4 movement and R214W changes the VSD-PD coupling such that channel opening only occurs after all voltage sensors have moved. Because KCNQ2 channels play a pivotal role in controlling neuronal excitability, our findings uncovering the dynamics and statedependent molecular rearrangements that lead to channel gating, will be central to understanding how channelopathies alter neuronal function. Understanding how mutations affect channel activity through different mechanisms can lead to better ways to correct these mutational defects.
Using a state-dependent cysteine modification approach, we map the extracellular boundaries of S4 residues during membrane depolarization. Our cysteine accessibility data suggests that a had now moved about three helical turns outward (upward) from F137 into a position close to or within the extracellular space(22) (Figure 1-figure supplement 3B). These rearrangements are in line with our cysteine accessibility data in which residues N-terminal to residue F202 become exposed in the activated state of S4 at strong depolarizations ( Figure 1-figure supplement 3C, D).
This relatively large outward motion of S4 is consistent with our estimated total gating charge of 7.37 e0 per channel moved during KCNQ2 activation gating. Compared to the charges moved during gating of the Shaker K + channel (12 to 14 elementary charges per channel (27,28,47,48)), our estimates seem low. However, compared to the 7 arginines present in S4 of Shaker, the S4 of KCNQ2 channels has only 5-6 arginines, with the third one (R3-like) being a glutamine conserved across KCNQ channels. Interestingly, in Shaker channels, R3 seems to contribute around 1 e0 per subunit (4 e0/channel) (28), which may explain why in KCNQ2 channels (with R3 substituted by glutamine) the calculated equivalent electronic charges moved across the membrane is less than the value of Shaker channels. Compared to the total charges moved during gating of related KCNQ1 channel (4.13 e0 per channel)(49), the 7.37 e0 per KCNQ2 channel activation seems slightly bigger.
However, in contrast to KCNQ2 channels, KCNQ1 only has 3 arginines in S4, with the third one (R5like) being a histidine. Overall, our data suggests that S4 of KCNQ2 channels undergoes similar movement to that of KCNQ1 and Shaker K + channels.
We found that the fluorescence signals from labeled F192C track conformational changes of S4 in KCNQ2 channels. VCF shows that both the steady-state voltage dependence of S4 transitions and the kinetics closely follow those of ionic currents, which concurrently had virtually no delay and exhibited no sigmoidal time course. These findings indicate that S4 does not necessarily require independent conformational changes in all four KCNQ2 subunits before channel opening as shown for classical voltage-gated K + channel from the squid giant axon (50). Instead, these close correlations in time and voltage dependence of fluorescence and current support a gating scheme in which either the S4s move concertedly to open the channel, or individual voltage sensor movement might be sufficient for pore opening similar to that proposed for KCNQ1 (without KCNE1) channels (36,51).
Based on our KCNQ2 data, we cannot distinguish between concerted or individual S4 movement, which will require additional experiments that are out of the scope of this work. Using VCF on linked concatemers of KCNQ1 subunits, it was shown that all four voltage sensors move independently, and channel opening can proceed before all voltage sensors have moved (51). Subsequent studies on KCNQ1 refined this initial model and further showed that the S4 can adopt resting-and intermediatestates at negative voltages before reaching a fully activated state at depolarized voltages, and that pore opening can occur from either S4 states (37,38). Additionally, these functional distinctive S4 configurations changed the ion permeation properties of KCNQ1 pore since the intermediate state showed a higher Rb + /K + permeability ratio than the fully activated S4 state (37 Here, we explored whether KCNQ2 channels also change their ion-permeation properties to get insight into pore conformations. We reason that if KCNQ2 channel opening also occurs with S4 in the intermediate state, the Rb + /K + permeability ratio would be lower in the mutant R214W that dissociates voltage sensor movement from channel opening ( Figure 6F, dashed maroon arrow) than in the wt-KCNQ2 channel, much like the effect of KCNE1 on KCNQ1 pore. However, we find very similar Rb + /K + ratios for both wt (0.52 ± 0.016) and the R214W mutant (0.51 ± 0.024) ( VCF data from KCNQ2* channels bearing the S4 charge neutralization mutant R198Q also supports the notion that the fluorescence signal tracks conformational changes of S4 coupled to channel opening. The de novo mutation R198Q in KCNQ2 channels has been previously reported to cause infantile spasms with hypsarrhythmia and encephalopathy associated with severe developmental delay (43). Compared with KCNQ2*, KCNQ2*-R198Q channels display left-shifted G(V) and F(V) curves and faster activation and slower deactivation kinetics of current and fluorescence ( Figure 5B, C and Figure 5-figure supplement 1A, B), as if the R198Q mutation directly affect S4 movement. Since R198Q seems to ease channel opening by simply altering the voltage sensor, and seemingly not by increasing ionic conductance, this might have potential therapeutic interest as drugs designed to target the S4 in a manner that rightward shifts its voltage dependence could decrease channel opening. Of note, our study did not aim to mechanistically explain how gainof-function mutations like R198Q cause epilepsy in vivo, which would further require the expression of combined wild-type and mutated subunits to mimic the heterozygous state, ideally using inhibitory and excitatory networks of neurons.  (22,53,54). Interestingly, the cryo-EM structure of KCNQ1 and KCNQ4, which captured PIP2 bound to these channels, showed that PIP2 localizes close to the S4/S4-S5 interface, in a positively charged pocket proposed to be a binding site for the negatively charged PIP2. Taking advantage of these findings, we superimposed the existing KCNQ2 structure (22) with homologous structure of KCNQ1 bound to PIP2(53) (Figure 5-figure supplement   2B). We noted that residue R214 (together with the adjacent R213 residue) lies very close to PIP2, raising the possibility that R214 in the KCNQ2 channel could also be part of the positively charged pocket that coordinates PIP2 binding ( Figure 5-figure supplement 2B). Previous studies in KCNQ1 and KCNQ3 channels have shown that PIP2 directly affects the VSD-PD coupling since PIP2 depletion from the membrane impeded pore opening without affecting S4 movement (42,55). However, the molecular details by which PIP2 mediates VSD-PD coupling is still the subject of ongoing debate. Based on our VCF results shown in Figure 5D, E that suggest that R214W mutant would dissociate S4 movement from channel opening, we hypothesize that the positive charge of residue R214 is crucial for PIP2 binding. We propose that in KCNQ2, PIP2 may act like a molecular "glue" that tightly ties the loop connecting S4 and S4-S5 linker such that during depolarization, the S4 movement effectively pulls S4-S5 away from the pore domain to activate potassium conductance.  (Figure 1-figure supplement 2). A computer-driven valve controlled a home-made perfusion system that allowed for a rapid switching (within 2 s) between ND96 and MTS-reagents during either the open or closed protocol.
We adapted the open and closed state protocols (26) to study the solvent exposure of the substituted cysteines (cys) in S3-S4 and S4 and test whether these cys-residues were exposed in open and/or closed channels using irreversible covalent modification by MTS reagents ( Figure 1B).
Briefly, cells were held at −80 mV for 1-s before stepping to +20 mV for 12-s, then repolarized for another 12-s to −80 mV (for the open state) or voltages between −80 and −140mV (for the closed state), before stepping to the test potential (+20 mV) to measure the change in currents induced by several 5-s cycles of MTS-reagents (see black rectangles in Figure 1B CaCl2, 1 mM MgCl2, 5 mM HEPES); pH = 7.5. Rb + /K + permeability ratios were determined using inward tail current measured at −60 mV following the 2-s activation pulse at +60 mV. Inward tail currents were determined following normalization of outward current to calculate Rb + /K + ratio.
Modelling. Fluorescence and current from wt-KCNQ2 and mutated KCNQ2 channel models were simulated using Berkeley Madonna software (Berkeley, CA, USA), similar to the allosteric model initially proposed for KCNQ1 channels (36). In our KCNQ2 model, rate constants for each transition were of the form ki = ko x exp(-zi(V)/kT), where ki and zi were determined from data in Figure 3 and where A1 and A2 are conductances that would be approached at extreme negative or positive voltages, respectively, V1/2 the voltage that activates the conductance (A1+A2)/2, and z is an apparent valency describing the voltage sensitivity of activation (e is the electron charge, kB the Boltzmann constant, and T the absolute temperature). Due to the generally different numbers of expressed channels in different oocytes, we compare normalized conductance, G(V): Fluorescence signals were corrected for bleaching and time-averaged over 10-40 ms intervals for analysis. The voltage dependence of fluorescence f(V) was analyzed and normalized (F(V)) using relations analogous to those for conductance (equations. 1 and 2).

Statistics.
All experiments were repeated 4 or more times from at least three batches of oocytes.
Pairwise comparisons were achieved using Student's t test or ANOVA with a Tukey′s test. Data are represented as mean ± SEM (standard error of mean) and "n" represents the number of experiments.      resting state (C) becomes exposed to the extracellular space (green spheres) in the activated state (D). The four subunits are shown as ribbons and buried and extracellularly exposed residues in the S4 are shown as red and green spheres, respectively. Dotted lines indicate the proposed inner and outer lipid bilayer boundary. PDB code for KCNQ2: 7CR0. All images were generated using UCSF ChimeraX, version 1.1 (2020-10-07).      Table 2. Parameters for model in Figure 6. L represents an allosteric coupling factor associated with the backward rates in the model of Figure 6F. The gating charges z associated with each transition were determined from fits of the data in Figure 3, where ki = ko x exp(-zi(V)/kT).